Let's start by just first dispatching with the idea that there were only two options — "do it exactly as they did it" (which means two nukes, on cities, no warning, spaced out by only 3 days, early August) and "a full American invasion" (scheduled for November). There were other options on the table, and even the original "schedule" is not what happened in reality (there was supposed to be a full seven days between the first two bombings). This isn't to say that any of these alternatives are necessarily more favorable or desirable or "should have been done" — it is just to say that when you are forced into a false dilemma between two choices, it polarizes all discussion around questions that frankly I think are distractions, like "what were the casualty figures that Truman himself heard, versus what others came up with?" This is kind of an irrelevant question (the answer to it is, "he was told a fairly low figure for invading Kyushu and the Kanto Plain — 40,000 deaths — but they did have other estimates, and Truman didn't inquire because he either didn't care or it was irrelevant to the atomic bombing issue"), because even at the time there was no view of it being about "bomb or invasion," it was about "what exactly do you do with the bomb, and if that or the Soviet declaration of war doesn't lead to surrender, then we'll invade." Or to put it another way, it was never "bomb or invasion," it was "bomb and Soviets and invasion." Only after the war ended, and there started to be criticism of the bombings, did the narrative of "we had to do this because we were certain it would not require an invasion if we did" come about. (Specifically, this "orthodox" justification of the bombings takes its full form around 1947, in an article in Harper's that ran under the name of the former Secretary of War, Henry Stimson, but was largely authored by General Groves, the person who ran the atomic bomb project.)

Putting that aside, I would note that most professional historians would characterize Zinn's approach as being a bit overconfident in his counterfactual scenario. Were the Japanese on the ropes? Oh, yeah. That was very clear. But "defeated" is not the same thing as "surrendered," and the difference does matter.

Would an invasion have been necessary, if the bombs hadn't been used? That's a tough counterfactual to wrestle with, even knowing much more today than they did back then about what the various factions of the Japanese high command were thinking at the time. But it is worth noting that the idea that the bombs weren't necessary isn't actually just one that comes from far-left, latter-day historians like Zinn. The US Strategic Bombing Survey, in 1946, concluded that:

Based on a detailed investigation of all the facts, and supported by the testimony of the surviving Japanese leaders involved, it is the Survey's opinion that certainly prior to 31 December 1945, and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated.

Now, did the USSBS authors have an axe to grind? You bet — their report is all about how it was all of the other bombing that had reduced Japan to such a fragile state that the "dual shock" of the atomic bombs and Soviet invasion would cause them to finally throw in the towel. This is one of the reasons (alluded to in another comment) that many military leaders at the time thought the bombings of Hiroshima and Nagasaki were unnecessary — because the atomic bombs were getting too much credit for winning the war. They were afraid that if people started thinking the atomic bomb was all you'd need, you'd be tempted to downsize the military in a drastic way, to put all your reliance on nuclear weapons. Which, in fact, Truman attempted to do... until the Soviets set off their own atomic bomb. Eventually, as we all know, the military got awfully chummy with the nuclear complex and learned to love the bomb, but that took some time.

My feeling — and this is about personal experience in talking with a lot of historians and going to a lot of conferences and workshops and panels and whatnot — is that most professional historians who work specifically on this topic would dodge the question, pointing out that "necessary" and "justified" are both normative and counter-factual terms (and both of those things make historians uncomfortable), or would lean towards a "they were going to use the bombs anyway, there was no 'decision' or debate at a high level, so this is an anachronistic question to ask" (which, I might say, I would point out is a problem with asking the wrong question — there was, as far as we can tell, no "decision to use the bomb," but there were many smaller, but important, "decision_s_" about how to use it, and that is what a few threads of my own research are about).

But if you cornered them... held a gun to their head... really demanded they take a stand... I think the lot of them would be pretty split. The way I see the field these days is a lot of hovering around a "middle" position on the bombs, as opposed to the extreme "ends" of the spectrum ("totally justified, best decision ever" vs. "terrible war crime done just to look tough"). The authors you are quoting, like Zinn (and Kuznik, who is also quoted by another response), are I think pretty anomalous in that they still stake out a hard, confident position on one end of the spectrum. (There are a few who stake out the other end, too.) The "middle" position, what the historian J. Samuel Walker calls "the consensus view", basically says that the bombs were seen as a perfectly fine, if not a little unusual, military decision, that they might not have been solely responsible for the surrender of Japan, and that the use of the bombs in the way they were used (on cities, little spacing, early August) was a mixture of vaguely strategic thinking (no "grand plan" on anyone's part, but people did have some ideas about what you might get out of doing it that way) and complete happenstance (the spacing between the bombs, and the fact that they had two ready to go in early August, depended on external factors that had nothing to do with real strategy).

The "middle" view would, like the "pro-bomb" view, emphasize the context of the war and firebombing (destroying cities was not a new thing at that point), but, like the "anti-bomb" view, emphasize that choices were made, and that it's not easy to say one way or the other whether the bombs "ended the war." It's a position designed to satisfy nobody, in the end, because it doesn't make the bombings either a triumph of American decision-making (as the "pro-bomb" historians would have it), or an example of the maliciousness of American hegemony (as the "anti-bomb" historians would have it). It doesn't really satisfy any particular political agenda, because in the end it is saying that everything was kind of muddled up and haphazard.

I prefer the latter view, obviously, in part because it conforms with my own view of human nature and human governance — messy and without very many obvious moral narratives. I would take some aspects of this a bit further, and have in my own writing — I think Truman did not really understand what was going on, in many respects, and I think most people underestimate exactly how haphazard some aspects of the bombings were (the Nagasaki raid in particular, which was a near-disaster and exemplifies the limits of trying to impose a grand-strategy narrative onto the bombings). But this is work-in-progress, so take it as you will.

I would also note that this entire field of study is marred by over-reliance on post-facto sources (e.g. memoirs), which, given the explicit politicization of the "decision to use the bomb" and every aspect of it, tend to reflect more about how the memoir writer later saw things, and not so much about what they were thinking at the time. In some places we have some very useful sources about what was going on at the time (memos, telegrams, diary entries, sometimes even recorded telephone conversations) that paint a far less orderly picture than the memoirs do. It is a tricky methodological problem, because as historians we do often have gaps in the archival record, and it is always tempting to "fill those in" with something from a memoir. But it can lead one down the wrong path, because you can "fill in" with the assumptions about what people were thinking (or knew) that lead to whatever broader argument you are aiming at in the first place. For my own part, the two things I always try to emphasize, both to students but even when talking with other scholars, is that we can't take for granted that people knew things (knowledge is tricky, and even if you "know" something you might not know it the way that we do later), and we need to make it really clear where we're taking a leap that gets us beyond an archival source. Taking interpretive leaps is fine — it's part of doing the job. But we should make it very clear where we are doing it, both to ourselves and to our readers, and not paper it over with "maybes" and "perhaps" sorts of clauses.

That article by Christian Appy is one of the prime examples of why one needs to look at primary sources and the context of said sources, and not just news articles/opinion pieces regurgitating facts from other sources.

For instance, in that very article, he quotes:

n fact, six of the seven five-star generals and admirals of that time believed that there was no reason to use them, that the Japanese were already defeated, knew it, and were likely to surrender before any American invasion could be launched. Several, like Admiral William Leahy and General Dwight Eisenhower, also had moral objections to the weapon. Leahy considered the atomic bombing of Japan “barbarous” and a violation of “every Christian ethic I have ever heard of and all of the known laws of war.”

The actual source he links to is The Untold History of the United States by Oliver Stone and Peter Kuznick. Nowhere does he actually mention the context of the quotes showing opposition.

For instance, his quote about Fleet Admiral Leahy's opposition comes from the book I Was There by Admiral Leahy, and it must be tempered with the fact that his actual quote says:

It is my opinion that the use of this barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. The Japanese were already defeated and ready to surrender because of the effective sea blockade and the successful bombing with conventional weapons.

As you can see, being a Navy guy, he emphasized quite heavily the fact that naval means could have beat Japan by blockading the country. Nevermind that a blockade would induce starvation in the Japanese homeland, which isn't indiscriminate - it in fact would disproportionately kill the elderly and the weak and civilians, as food supplies were already provided to fighters first.

Likewise, many quotes regarding opposition only came about after the war ended, when the debate was raging hot in the newly created Department of Defense about the importance of the Air Force and atomic weaponry. The Navy, Marines, and Army all opposed the heavy focus on atomic bombs and strategic bombing, and so it was at the very least politically advantageous to downplay the importance of the atomic bomb and remind people of the importance their branches played in the fight against Japan.

It wasn't until the conventional nature of the Korean War, and the fact that atomic bombs were not going to be allowed to be used in that war, that the importance of the other branches was brought to the forefront of defense planning again.

Also, Christian Appy provides zero sources for his claim that military experts only estimated 40,000 casualties for the invasion of Japan. The invasion of Okinawa, an island a fraction of the size of Japan and a fraction of the opposition forces or civilian population, had cost the US over 12,000 KIA and 55,000 wounded, and the Japanese had suffered even more: anywhere from 75,000-110,000+ killed.

Short of the Japanese putting down their arms and ceasing all fighting, it would have been impossible to have estimated only 40,000 casualties for a 3 month+ operation. It is also important to note that when they met in Potsdam, Truman and Marshall knew that total U.S. casualties were approaching the 1.2 million mark, the bulk having occurred in just the previous year.

Not to discourage additional discussion, but [the FAQ has an entire section on the atomic bombings of Japan] (https://www.reddit.com/r/AskHistorians/wiki/wwii#wiki_the_atomic_bombs.2C_aka_questions_.2Fu.2Frestricteddata_has_answered). Much of it discusses the "was it necessary, was it a good idea?" aspect of it.

I'd especially recommend ["Did the US have to nuke Japan in WWII?"] (https://www.reddit.com/r/AskHistorians/comments/2todt6/did_the_us_have_to_nuke_japan_in_wwii/) as it has additional links for questions very similar to yours.

Your question is the third rail of history, so there's lots of intelligent discussion about it on this sub.

The discussion here seems to overlook a key element in Japan's surrender decision. Japan didn't surrender unconditionally when Hiroshima was bombed. It didn't surrender unconditionally when the USSR declared war and invaded Manchuria. It didn't surrender unconditionally when Nagasaki was bombed. Instead it surrendered quasi-unconditionally after the US government indicated on August 12 that the Japanese throne would survive.

Even after the second bombing, Japanese top-level deliberations remained focused on protecting the throne. The August 10 Imperial Conference cabled Allied governments that

The Japanese Government are ready to accept the terms enumerated in the joint declaration which was issued at Potsdam on July 26th, 1945, by the heads of the Governments of the United States, Great Britain, and China, and later subscribed to by the Soviet Government, with the understanding that the said declaration does not comprise any demand which prejudices the prerogatives of His Majesty as a Sovereign Ruler.

This wasn't going to fly in Washington. The Potsdam Declaration had specified that there should be "established in accordance with the freely expressed will of the Japanese people a peacefully inclined and responsible government".

Secretary of State Byrnes was against any explicit modification of "unconditional surrender", let alone one that would leave the Emperor's powers intact. It was Navy Secretary Forrestal who broke the deadlock by proposing a more oblique form of words. Byrnes's reply of August 11 (received in Tokyo on the 12th) included the key provisions:

From the moment of surrender the authority of the Emperor and the Japanese Government to rule the state shall be subject to the Supreme Commander of the Allied powers who will take such steps as he deems proper to effectuate the surrender terms. The ultimate form of government of Japan shall, in accordance with the Potsdam Declaration, be established by the freely expressed will of the Japanese people.

"The authority of the Emperor... shall be subject" gave Hirohito just enough to overrule his military hawks and announce his decision to accept the clarified terms at the August 14 Imperial Conference.

So far, so good. One might conclude from this account that the bombings and/or the Soviet intervention were necessary to force Japan's rulers into an offer of surrender sufficient to elicit the required clarification of some postwar place for the throne.

The problem is that the clarification was itself substantially a return to the position proposed to Truman on July 2 by his "committee of three" (Grew, Stimson and Forrestal" as paragraph 12 of their proposed surrender ultimatum:

The occupying forces of the Allies shall be withdrawn from Japan as soon as our objectives are accomplished and there has been established, beyond doubt a peacefully inclined, responsible government of a character representative of the Japanese people. This may include a constitutional monarchy under the present dynasty if it be shown to the complete satisfaction of the world that such a government will never again aspire to aggression.

It was Byrnes who prevailed upon Truman to leave out the reference to the monarchy as they journeyed to Potsdam. Article 12 of the July 26 ultimatum retained the peaceful representative government but omitted all reference to the throne, the one thing that Hirohito and his advisers agreed must be preserved as they discussed surrender in the second week of August.

Invasion and bombing weren't the only alternatives available in July. It's impossible to know whether a more acceptable version of the Potsdam Declaration would have secured an earlier surrender. But it's also impossible to say that the bombings were necessary, or even that they or Soviet intervention ended the war.